In 1979 tapes were sent to West Yorkshire Police by a man claiming to be the serial killer who goaded detectives for their inability to catch him.
The hunt for the hoaxer, thought to be from Wearside in the north-east of England, diverted police resources from the real killer, Peter Sutcliffe, who is now serving life for the murders of 13 women.
Leading voice expert Dr Peter French used the latest technology to make the man sound as he would today, in a new bid to uncover his identify.
Dr French said: "If we were to make the assumption that the person was in their early- or mid-thirties and if they followed the general trend then this is what their voice might sound like today."
No action
The results of the voice aging technique will be heard on the ITV programme Real Crime: The Hunt for Wearside Jack, on Wednesday.
Programme makers Granada said they hoped the reconstructed voice would finally help catch the hoaxer.
But West Yorkshire Police have said that, "after careful consideration", they will be taking no further action.
"Much effort was placed into this aspect at the time of the original investigation and since, without success," said a spokesman.
"If we receive evidence on which we can act rather than suspicions based upon the sounds of someone's voice then we will take positive action."
Focus shifted
Patrick Lavelle, news editor of the Sunderland Echo and author of a book on the hoax, told BBC News Online its effect on the investigation had been dramatic.
He said: "It completely shifted the focus of the whole investigation from West Yorkshire to Wearside.
"It concentrated inquiries on Wearside for 18 months and during that period [Sutcliffe] was questioned and eliminated nine times. One of the reasons was that he didn't have a Wearside accent."
Part of the reason police officers became so convinced the hoaxer was the killer was because they incorrectly attributed the 1975 murder of Joanne Harrison in Preston, Lancashire, to the Ripper.
Mr Lavelle is convinced the hoaxer and the Preston murderer are the same person.
Distinctive accent
The hoaxer's accent was eventually traced to the Castletown area of Wearside and most of the male population was interviewed as police descended on it.
Mr Lavelle added: "A couple of marriages broke up because of it.
"It was such a distinctive accent and such a shock for people to be told there was a serial killer living in their midst."
Mr Lavelle said details of a potential suspect in the hoax passed to Lancashire Police had been dismissed as "information rather than evidence".
"My opinion is that the police don't want to catch them."